After watching this @numberphile video I wanted to give it a try.

Then I came up with this piece if python code to try to find a possible 12 iteration sequence.

```
def factors(nr):
i = 2
factors = []
while i <= nr:
if (nr % i) == 0:
factors.append(i)
nr = nr / i
else:
i = i + 1
return factors
def per_internal(iteration, number, doPrint = False):
if doPrint:
print '{} {} {}'.format(iteration, number, factors(number))
if len(str(number)) == 1:
return iteration
digits = [int(i) for i in str(number)]
result = 1
for digit in digits:
result *= digit
return per_internal(iteration + 1, result, doPrint)
def per(number, doPrint = False):
return per_internal(0, number, doPrint)
for x in range(0, 54):
for y in range(0, 54):
for z in range (0, 54):
candidate = 2**x * 3**y * 7**z
iterations = per(candidate, False)
if iterations >= 10:
per(candidate, True)
```

Result:

```
0 937638166841712 [2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7]
1 438939648 [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 7, 7]
2 4478976 [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3]
3 338688 [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 7, 7]
4 27648 [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3]
5 2688 [2, 2, 2, 2, 2, 2, 2, 3, 7]
6 768 [2, 2, 2, 2, 2, 2, 2, 2, 3]
7 336 [2, 2, 2, 2, 3, 7]
8 54 [2, 3, 3, 3]
9 20 [2, 2, 5]
10 0 []
0 4996238671872 [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7]
1 438939648 [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 7, 7]
2 4478976 [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3]
3 338688 [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 7, 7]
4 27648 [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3]
5 2688 [2, 2, 2, 2, 2, 2, 2, 3, 7]
6 768 [2, 2, 2, 2, 2, 2, 2, 2, 3]
7 336 [2, 2, 2, 2, 3, 7]
8 54 [2, 3, 3, 3]
9 20 [2, 2, 5]
10 0 []
```

Just put the prime factors after each other and you have your initial number.

You don’t have to search any further because 222222222222222222222222222222222222222222222222222222 is the

Below this number, no numbers are found that create a 12 number sequence.

Sorry Matt,

11 is the max